Toroidal Momentum Pinch Velocity due to the Coriolis Drift Effect on Small Scale Instabilities in a Toroidal Plasma

Abstract

In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.

Poloidal rotation and its relation to the potential vorticity flux

“…͑18a͒ and ͑18b͒. The perpendicular stress as well as the first contribution to the parallel stress can be recognized as E ϫ B convection of perpendicular 11,31 and parallel momentum, [32][33][34][35] respectively. The second contribution to Eq.…”

Electromagnetic effects on toroidal momentum transport

“…This parallel momentum can, for practical purposes, be used as an approximation for the toroidal momentum. Recently, symmetry breaking effects of toroidicity were also found, [12][13][14]16 which are usually stronger than those caused by the flow shear on the eigenfunction. [7][8][9][10][11] A recent review on theoretical developments and experimental analysis of momentum transport and rotation can be found in Ref.…”

“…This discrepancy could be resolved as suggested by various studies through the existence of momentum pinch ͑inward flow of momentum flux͒, which is anticipated as the result of symmetry breaking effects on toroidal momentum transport. [7][8][9][10][11][12][13][14][15][16][17][18] The first effect of this type 8,9 was identified as the effect of an asymmetric eigenfunction on the average of the parallel mode number which is needed for the parallel momentum transport. This parallel momentum can, for practical purposes, be used as an approximation for the toroidal momentum.…”

Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas

“…24 On the theoretical front, there has been a multitude of attempts to explain this phenomenon. Note that an inward convective flux of momentum [25][26][27] ͑i.e., a "momentum pinch"͒ that transports scrape-off layer ͑SOL͒ flows into the core, cannot explain the L-H spin-up, since the direction of the SOL flows can be changed by changing the location of the x-point ͑or where the plasma touches the wall͒, yet the direction of the H-mode rotation in the core remains unaltered. 28 A theory that has some possibility of explaining this phenomenon is based on "residual" Reynolds stress 29,30 ͑or more generally, a residual component of the toroidal stress tensor͒.…”

“…Parallel flow shear itself, 36 magnetic curvature ͑curvature from B ʈ ‫ء‬ in laboratory frame͒, 26 or the effect of Coriolis drift in rotating frame, 25 can also lead to k ʈ symmetry breaking but give diffusive and pinchlike contributions to the Reynolds stress. Here we only consider the truly off-diagonal ͑i.e., residual͒ terms, which do not contain the transported field itself, since only these can explain the formation of a nonvanishing field from an initial value of zero, or the anomalous residual "torque" that acts on the plasma when the field and its gradients are set to vanish.…”